Evolution, 4th Edition

112 CHAPTER 5

fitness by 0.1 percent, then s = 0.001 and it will take about 4000 generations for A 2

to spread through the population. This shows that a minute fitness advantage will

cause large evolutionary change in a geologically short period of time. If selection

is 100 times stronger, then the beneficial allele has a 10 percent fitness advantage

and s = 0.1. The allele frequency changes 100 times faster, and the favorable allele

spreads through most of the population in only about 40 generations. To show

that there is a fitness difference of 10 percent would require measuring fitness on

hundreds of individuals. Yet even a difference of that size can cause evolution fast

enough to be directly observed. For the peppered moth, with a generation time of

1 year, a noticable change in the population took just a few years. For a bacterium,

whose generation time might be measured in hours, that change can take just a

few days.

The rate at which positive selection causes an allele frequency to evolve depends

on dominance. An allele is dominant if it causes the same phenotypic effect when

heterozygous as when homozygous. (Dominance does not refer to an allele’s fre-

quency in a population.) Up to this point we have been discussing alleles that do

not have dominance: the heterozygote’s fitness has been intermediate between the

fitnesses of the two homozygotes. If allele A 2 is dominant and beneficial, it will ini-

tially spread even more quickly than what we saw previously (FIGURE 5.10). W hen

A 2 is rare (as when it first appears by mutation), almost all copies of it are in hetero-

zygotes. That fact follows from the Hardy-Weinberg ratios. For example, with an

allele frequency of 0.01, the frequency of heterozygotes is 2 × 0.01 × 0.99 = 0.0198,

while homozygotes are almost 200 times more rare: (0.01)^2 = 0.0001. A dominant

beneficial mutation spreads more rapidly when rare because heterozygotes share

the full fitness benefit that the homozygotes have. The situation reverses, how-

ever, when allele A 2 is common. Now the low-fitness A 1 A 1 homozygotes are rare,

and almost all individuals have high fitness. Because there is so little variation in

Futuyma Kirkpatrick Evolution, 4e

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(A)

100 200 300 400 500

s = 0.05

88 Generations

0.2

0.4

0.6

0.8

1.0

0

Generation

Frequency of

A

2

(B)

100 200 300 400 500

s = 0.02

220 Generations

0.2

0.4

0.6

0.8

1.0

0

Generation

Frequency of

A^2

FIGURE 5.9 The time needed for a beneficial allele to spread through a population is

inversely proportional to the strength of selection. When the mutation has a selection coef-

ficient s and heterozygotes have intermediate fitness, it takes roughly 4/s generations for

the mutation to increase in frequency from 10 percent to 90 percent. (A) The trajectory for

a mutation that increases fitness by 5 percent. Here s = 0.05, and the time needed will be

about 4/s = 80 generations. The exact time taken is a bit longer: 88 generations. (B) The

trajectory for a mutation that increases fitness by 2 percent. Now s = 0.02, and the time

needed will be about 4/s = 200 generations. The exact time needed is 220 generations.

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